Finding magnitude and direction of net force on a dipole.

[jlmccart03]

Homework Statement

A dipole with charges ±q and separation 2a is located a distance x from a point charge +Q, oriented as shown in the figure.

Part A:
Find an expression for the magnitude of the net force on the dipole in the limit x≫a.

Part B:
What is the direction of the net force? Enter answer as number of degrees counterclockwise from the positive x-direction.

Homework Equations

F = kq₁q₂/r²

The Attempt at a Solution

I honestly cannot think of a solution for this problem. Currently I am stuck on the dipole piece. How does one come up with an equation using the limit x >> a? I guess a better question would be what that means in terms of figuring out the net Force on the dipole. I am simply confused on where to start or how to begin besides using F = kq₁q₂/r²

 

[haruspex]

F = kq₁q₂/r²

Mostly, students start with an equation they have learned specifically related to dipoles. I cannot tell whether you are expected to start from there or from the equation you quoted. Either will do, but it is a bit more work using the latter. Since that's the equation you quote, I'll assume for now that is the method to use.

If you were asked to find the force the dipole exerts on the point charge, could you do that?

 

[jlmccart03]

Mostly, students start with an equation they have learned specifically related to dipoles. I cannot tell whether you are expected to start from there or from the equation you quoted. Either will do, but it is a bit more work using the latter. Since that's the equation you quote, I'll assume for now that is the method to use.

If you were asked to find the force the dipole exerts on the point charge, could you do that?

Well the dipole exerts both a positive and negative force onto the +Q charge which would simply cancel out correct? Since they are equidistant thus equal, but opposite magnitudes.

 

[haruspex]

Well the dipole exerts both a positive and negative force onto the +Q charge which would simply cancel out correct? Since they are equidistant thus equal, but opposite magnitudes.

The two forces are not quite in the same direction, so they do not quite cancel. It's the little bit of force remaining that is of interest.

 

[Cutter Ketch]

The diagram might make you think the charge is spread out over the dipole, but when they say separated by 2a they are telling you to treat them as point charges.

Treat the dipole as a rigid body in two dimensions. It has two forces acting on it. Draw a free body diagram, resolve the forces into their components, write the net force components and see if it approximates to something simpler as x becomes much larger than a.